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27 May, 15:42

Which do you prefer: a bank account that pays 5 %5% per year (EAR) for three years or: a. An account that pays 2.5 %2.5% every six months for three years? b. An account that pays 7.5 %7.5% every 18 months for three years? c. An account that pays 0.5 %0.5% per month for three years?

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  1. 27 May, 16:05
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    c. An account that pays 0.5 %0.5% per month for three years.

    Explanation:

    We can evaluate all the option using following formula:

    EAR = (1 + (r / m)) ^m - 1

    a.

    2.5% every six months for three years

    r = 2.5% = 0.025 / 6 =

    m = 12/6 = 2

    EAR = (1 + 0.025) ^2 - 1

    EAR = 0.050625 = 5.06%

    7.5% every 18 months for three years

    r = 7.5% for 1.5 years = 7.5% / 18 = 0.4167% per month = 0.004167 per month

    EAR = (1 + 0.004167) ^12 - 1

    EAR = 0.051166 = 5.12%

    0.5% every month for three years

    r = 0.5% = 0.005

    EAR = (1 + 0.005) ^12 - 1

    EAR = 0.0616778 = 6.17%

    We will prefer an account that pays 0.5 %0.5% per month for three years, it pays the highest return.
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